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Outside the Classroom:

Evidence on Non-Instructional Spending and Student Outcomes*

Lucy Sorensen

Sanford School of Public Policy, Duke University

Draft Prepared for Annual AEFP 41st Annual Conference

Denver, CO, March 17-19 *Work on this paper was supported by a pre-doctoral fellowship provided by the National Institute of Child Health and Development (T32-HD0736) through the Center for Developmental Science, University of North Carolina at Chapel Hill. The author is grateful for data assistance from the North Carolina Education Research Data Center (NCERDC) and the North Carolina Department of Public Instruction (NC DPI). The author would also like to thank Kenneth Dodge, Helen Ladd, Philip Cook, Marcos Rangel, and Joseph Hotz, for invaluable feedback.

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Abstract

Much prior research on school finance has assessed the relation between overall

funding of schools and student achievement outcomes. This study moves beyond the

simple bivariate association to contribute new evidence on how non-instructional

investments – such as increased spending on school social workers, guidance counselors,

and health services – affect multiple aspects of student performance and well-being.

Merging several administrative data sources spanning the 1996-2013 school years in

North Carolina, I use an instrumental variables approach to estimate the extent to which

local expenditure shifts affect students’ academic and behavioral outcomes. My findings

indicate that exogenous increases in spending on non-instructional services not only

reduce student absenteeism and disciplinary problems (important predictors of long-term

outcomes) but also significantly raise student achievement, in similar magnitude to

corresponding increases in instructional spending. Furthermore, subgroup analyses

suggest that investments in student support personnel such as social workers, health

services, and guidance counselors, in schools with concentrated low-income student

populations could go a long way toward closing socioeconomic achievement gaps.

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1. Introduction

A number of studies, with varying results, have examined the link between school

resources and student achievement (summarized in Greenwald, Hedges, & Laine, 1996;

Hanushek, 1997; and Verstegen & King, 1998). The central debate in this school finance

literature concerns whether increased education spending translates to higher student test

scores. This body of research, however, largely fails to consider how resources are

allocated across different functions within schools, or how increased spending may affect

students across a broader set of student outcome domains. The current study seeks to

address both of those topics, with particular attention to whether increased expenditures

on social workers, health services, and guidance services within schools contribute to

aspects of student well-being.

For the first time, in 2012 more than half of all U.S. students in K-12 schools

came from low-income families, defined as meeting the eligibility requirements for free

or reduced-price school lunches (NCES, 2013). Employers lament American

adolescents’ low high school graduation rates (despite recent improvements) and even

lower readiness to join the work force. At the same time, the rate of children and youth

with diagnosable mental health disorders in the U.S. has grown to over 20 percent, and

other health concerns for students such as obesity, allergies, and asthma continue to rise

(CDC, 2013). School systems across the country are considering the extent to which they

should provide support services for the types of challenges that students bring to the

classroom from outside of school, with little research-based evidence to help guide

policymakers’ decisions.

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Although salaries and benefits for teachers account for over half of public school

expenditures, spending on support services for students such as health, guidance, and

social work services has grown in prominence. Between the 1990-91 and 2010-11 school

years, inflation-adjusted per-pupil expenditures nationwide on student support services

increased by 66 percent (NCES, 2013, Table 236.60). The recession of 2008 altered the

upward trajectory of spending, and local districts responded in different ways by

curtailing spending for different purposes. The question of how this temporal and

geographic variation in the mix of type of education spending affects student academic

and behavioral outcomes has gone largely unanswered.

The current study focuses on the case of North Carolina, and involves two main

components. First, I examine descriptive trends in instructional and non-instructional

spending over the past 20 years. Second, I assess whether shifts in the levels of local

instructional and non-instructional spending affect students’ academic and behavioral

outcomes. The study relies on administrative data merged from several sources, spanning

the 1995-1996 through 2012-2013 school years.1 County-level education expenditures

by detailed purpose code and year come from the North Carolina Department of Public

Instruction (DPI). Student-level data on standardized test scores, absences, disciplinary

offenses, and extracurricular participation come from the North Carolina Education

Research Data Center (NCERDC).

In North Carolina, as in all other states, school funding derives from local

(26.2%), state (62.1%), and federal (11.7%) revenue sources. The state funds schools

with three basic types of allotments: position allotments, for which a certain number of

certified teachers and other educators are provided to local school systems and paid based                                                                                                                1 From this point forward, I will refer to this time period as from 1996-2013 for simplicity.

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on the state salary schedule; dollar allotments, which can be used to hire employees or

purchase goods for a specific purpose; and categorical allotments, which provide as much

funding as necessary to address the needs of a particular population or service. County

governments in North Carolina are responsible for fulfilling school facility requirements

and also for supplementing current operating expenses of the public school system

“within the financial resources and consistent with the fiscal policies of the board of

county commissioners” (North Carolina General Statutes, 2014, 115C-408). For this

study, I focus primarily on the impacts of local education expenditures based on two

considerations. First, county governments tend to have more flexibility in terms of both

their level of educational spending and also to which school resources they allocate

funds. Second, my identification strategy relies on quasi-random changes to local

revenues and governing bodies, which have no direct relation to state or federal spending.

This analysis uses an instrumental variable approach, taking advantage of

exogenous variation in county expenditures on different educational categories. This

variation in local education spending comes from two different sources. First, every

eight years (at a minimum) each North Carolina county must reassess property values.

When counties do so, they tend to experience sudden and sizeable increases in property

tax revenues, and a disproportionate amount goes to abrupt increases in local school

budgets. Because revaluation years differ across counties on a schedule that is

uncorrelated with county factors, I can use these within-county discontinuities at

revaluation year as quasi-random variation in local expenditures. Second, since boards of

county commissioners have direct control over both the level and types of funding for

education in North Carolina, changes in the political party majority of boards affect both

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total county expenditures and the amounts of resources allocated toward academic and

non-instructional educational purposes. This within-county measure of political change

therefore can serve as a second instrumental variable. (An interaction term between the

revaluation variable and the political variable serves as a third).

This analysis examines for the first time how shifts in absolute and proportional

school financing for non-instructional support services at the district level might

influence students’ development. It estimates causal effects of student support-services

expenditures on achievement and several “non-cognitive” outcomes (including

absenteeism, disciplinary infractions, and extracurricular participation) shown to be

predictive of long-term well-being (Jackson, 2012). Recent empirical research has

further emphasized the long-term importance of non-academic behaviors for educational

attainment, labor market outcomes, and social outcomes (Heckman, Stixrud, & Urzua,

2006). In estimating effects on both student achievement and behavioral outcomes, the

analysis uses a two-stage least squares approach alluded to above to address potential

empirical challenges: first, that district decision-making about budgetary allocations is

not random; and second, that there may be a time lag between current expenditures and

effects on student outcomes. (Specifically, to account for multiple endogenous predictor

variables, I use full information generalized two stage least squares estimates of a system

of simultaneous equations). The estimation models also control for concurrent spending

on other purposes, county and year fixed effects, detailed student-level covariates, and

county time trends.

Results show that increased spending on non-instructional services – including

social workers, guidance counselors, and health services – not only reduces student

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absenteeism and disciplinary problems, but also significantly increases student

achievement across all grades and subjects. In fact, the academic benefits of increasing

non-instructional resources at the county level match those of increasing instructional

salaries by the same amount. My findings indicate that spending only $100 extra per

pupil on non-instructional services could increase student test scores across various

subjects by between 0.014 and 0.099 standard deviations. By comparison, spending $100

extra per pupil on local salary supplements for teachers would increase average student

achievement by 0.016 to 0.078 standard deviations.2 Non-instructional spending

significantly outperforms instructional spending for math results, but the opposite is true

for reading.

These non-instructional effects on learning are substantially larger in schools with

high concentrations of poverty compared to those with lower concentrations of poverty,

with effect sizes in high-poverty schools up to 0.239 standard deviations (roughly

equivalent to average test score growth over the course of a school year) for an additional

$100 per pupil. This pattern suggests that investing in school support services and

opportunities for outside-of-school enrichment may hold greater value for students in

low-income communities. Such a robust effect for students in high-poverty schools

indicates that health and social services provision could be one low-cost policy option for

stemming the tide of widening socioeconomic achievement gaps (Reardon, 2011).

A potential mechanism is suggested by the fact that increased non-instructional

spending also significantly reduces student absences and serious disciplinary infractions.

$100 per pupil toward school support services translates to 0.58 fewer absences per                                                                                                                2  These values are presented as ranges of test score increases across four groups: math scores in grades 4-8, reading scores in grades 4-8, humanities scores in grades 9-12, and science scores in grades 9-12. Detailed findings by student subgroup are presented in the results section.  

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student per year and 0.99 fewer serious disciplinary infractions. If social workers,

truancy officers, or health services, for example, are capable of improving student

attendance and behavior indicators, then the mere fact that students are at school more

frequently, with fewer behavioral disruptions, could drive a large portion of the ultimate

effects on student learning. In fact, a simple mediation analysis reveals that reductions in

absences and disciplinary infractions explain up to 30 percent of the main effect of

instructional expenditures on student test scores and up to 88 percent of the main effect of

non-instructional expenditures.

Section 2 provides contextual information on prior research regarding both school

resources and the school finance landscape in North Carolina. Section 3 introduces a

simple model of local government decision-making for optimizing educational outcomes.

Section 4 describes the new dataset used in this study and the empirical approach for

estimating effects of non-instructional expenditures. Section 5 presents results. Section 6

discusses the relevance of these findings for education finance at the local, state, and

federal levels.

2. Background

Prior research on non-instructional school resources

The literature on returns to school resources has a long history, with a back-and-

forth debate centered on whether or not money matters. This often equates to whether

class size matters. Hanushek (1997) concludes from a meta-analysis that variation in

school resources within the typical range across districts is not consistently related to

student achievement, although Greenwald, Hedges, and Laine (1996) perform a similar

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meta-analysis with findings opposite to Hanushek’s primary conclusions. Many of the

earlier studies face empirical problems because cross-sectional studies generate biased

estimates of returns to school spending, though the direction of this bias is debated

(Haegeland, Raaum, & Salvanes, 2012).

I assert that the domains to which resources are allocated are as important as the

overall level of resources. This topic – impacts of non-instructional student services and

opportunities – has a much more limited evidence base, however. Dee (2005) finds at the

national level that instructional spending increases high school graduation rates, whereas

other types of spending have a small negative effect on graduation rates. Reback (2010a)

explores the effects of school counselor policies on student achievement and behavioral

problems. He finds that greater counselor subsidies reduce the frequency of disciplinary

incidents but do not strongly influence achievement. In another study (Reback, 2010b),

he finds that elementary counselors substantially influence teachers’ perceptions of

school climate, reduce the fraction of teachers reporting that their instruction suffers due

to student misbehavior, and reduce the fraction reporting problems with students

physically fighting each other, cutting class, stealing, or using drugs. Carrell and

Hoekstra (2011) conclude that one additional school counselor reduces student

misbehavior and increases boys’ academic achievement by over one percentile point.

These three papers resemble the motivation of the current study, but I use a different

identification strategy and consider other elements of non-instructional resources such as

school social workers and health services.

Researchers and education leaders increasingly recognize the potential value of

health services in schools, including through implementation of school-based health

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centers (SBHCs). Lovenheim, Reback, and Wedenoja (2015) examine the impacts of

providing primary care health services to students from low-income families (delivered

through SBHCs) and find large reductions in teen fertility, though no effects on high

school dropout rates. Although causal analysis on this topic is still thin, a sizeable

amount of work has demonstrated that poor health or adverse health events among

children are associated with worse long-run educational and economic outcomes (e.g.

Currie et al. 2010). Therefore, it logically follows that the provision of health services

within schools may prevent such adverse outcomes or have advantageous spillovers for

student learning.

The third main school resource of interest in this study, in addition to counselors

and health services, is school social work and attendance services. School social workers

serve as mental health providers for students and can assist in linking students and their

families to a variety of community services. There are currently no large-scale studies of

the effects of social work services in schools. However, prior research has evaluated a

variety of types of small-scale social work interventions. A meta-analysis of universal

and targeted social work interventions by Allen-Meares, Montgomery, and Kim (2013)

illustrates that many of these programs have positive effects in terms of student sexual

health, aggression, self-esteem, school attendance, identity, and depression.

A recent large-scale study by Jackson, Johnson, and Persico (2015) uses variation

in school spending from court-ordered school finance reforms to determine that increased

total per-pupil funding has large positive effects on students in high-poverty districts, but

smaller or nonexistent effects for students in more affluent districts. This finding could

reflect a number of factors. Relevant to the current study, though, it could support the

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hypothesis that certain services provided within schools – such as social workers,

guidance counselors, psychologists, and health services – are more valuable to students

whose families lack the means to pay for these services and other opportunities outside of

school. The current study will test this hypothesis more formally.

North Carolina school finance

Understanding the fiscal context of the North Carolina public school system is

essential for examining the role that non-instructional expenditures play in fostering

positive student outcomes. As in all states, funding for education comes from a

combination of federal, state, and local sources. In North Carolina, local revenues

account for about 26 percent of total education spending and a greater share of school

capital spending and salaries for non-certified personnel (NC DPI, 2015). Although the

current study examines the effects of aggregate spending (local, federal, and state) on

student outcomes, there tends to be greater flexibility and geographic variation in how

local funds are appropriated, and the local share of current education expenses has been

growing over time (North Carolina Center for County Research, 2015). For this reason,

research such as the current study aimed toward evaluating local education finance

decision-making holds immediate policy relevance.

An elected board of county commissioners is responsible for determining the

yearly public education budget for a given county and for allocating local revenues

among various educational and non-educational purposes. A majority of county revenues

in the 2013-2014 year originated from property taxes (51%), with the remainder coming

from sales taxes, sales and services, intergovernmental transfers, debt services, and other

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sources. The county commissioners allocate these local revenues toward a number of

different purposes: education (35%); public safety (20%); human services (20%); general

government (10%); and other categories (NCACC, 2015).3 In the domain of public

education, North Carolina counties are charged with building, equipping, and maintaining

school facilities and also with supplementing school operating expenses. They provide

current expense funds in a lump-sum annual appropriation to school districts. These

funds are typically used for teacher salary supplements, provision of non-certified

positions, and administrator positions. The fifteen city districts that exist within county

boundaries have no fiscal authority, and therefore are considered as a single unit together

with the rest of the county for this analysis. 4

Nationwide, 23.4 percent of operating expenditures nationwide in unified school

districts in 47 states are dedicated to non-instructional purposes (Dee, 2005). This

translates to around $935 per pupil for total non-instructional salary spending and $3,024

per pupil for total instructional salary spending. Larger, county-wide local education

agencies (LEAs) tend to allocate more money per student toward non-instructional

purposes than do smaller, community-centric LEAs (Deluca, 2015). In this study, I

define instructional spending as any direct salary expenditures on instructional services.

In North Carolina, the state pays teachers through a statewide standardized salary

schedule. All local instructional expenditures at the county level therefore are in the form

                                                                                                               3 These percentages reflect the average across North Carolina’s 100 counties; counties vary in their spending patterns. 4 Technically, the reality is more complicated. Counties are responsible for raising funds and allocating those funds to districts within the county. Counties generally allocate funds to particular purposes and functions, but school boards can amend these numbers by up to 25%. There is a back-and-forth budgeting process between school boards and county governments in which LEAs hire school personnel, establish salary supplements, and determine school facility needs, and the county is tasked with providing “sufficient” financial resources.

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of either salary supplements to the state-funded salary level or salaries for teaching

assistants.

I define non-instructional spending as any direct salary expenditures on 1)

guidance and psychological services; 2) social work and attendance services; and 3)

health services.5 Unlike with teachers, counties and local education agencies both have

the option of using local revenues to hire school personnel in these non-instructional

categories. These three expenditure categories have the practical advantage of being

measured consistently across the time period of interest (1996-2013), unlike other

purpose codes. They also reflect important aspects of students’ outside-the-classroom

development. Social workers address attendance issues and help students overcome

obstacles to learning that they may face in their homes or neighborhoods. Guidance

counselors often assist students in their personal and social development, and they

support students in building and achieving their long-term educational and career plans.

Health services can provide supplementary medical, dental, and nursing care.

Trends in spending in North Carolina

Education spending, in each of its various components, has grown and waned

during the past two decades in North Carolina. Both economic conditions and state and

federal political changes have driven much of this variation in school expenditures. In

Figure 1a, a binned scatter plot of county-year observations with a quadratic fit plot, we

observe that spending for instructional salaries rose between 1996 and the early 2000s,

but have experienced a steady decline since the 2004-2005 school year, brought on by                                                                                                                5 The exact purpose codes for these expenditures are: 5820 Attendance – social work services; 5830 Guidance services; and 5840 Health services. Exact descriptions of these categories are provided in Appendix Table A1.

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severe teacher salary cuts from the North Carolina state legislature and other cutbacks

due to the economic recession. One can notice that there are no important differences

between instructional spending patterns of high-poverty counties and those of low-

poverty counties.

On the other hand, for non-instructional spending we observe a large differential

between expenditures in low-poverty and high-poverty counties starting around 2005

(See Figure 1b). Low-poverty counties, defined as those with a median poverty rate of

school-age individuals between 1996 and 2013 lower than 25 percent, exhibited linearly

increasing expenditures on non-instructional support services (attendance and social

work, guidance and psychological services, and health services) across the time period.6

High-poverty counties display the same general trend, but with much higher per-pupil

expenditures on non-instructional services since around 2005. One potential driving

force behind this change was implementation of the Child and Family Support Team

Initiative (CFST). Beginning in 2005-2006, state funds supported one certified school

nurse and one licensed school social worker in each of 101 schools across the state with a

large proportion of high-risk students (Gifford et al., 2010).

Maps in Appendix Figure A1 illustrate both the temporal and geographic

variation in expenditures across North Carolina’s one hundred counties. Some of this

variation reflects state allotment policies: counties designated as “low-wealth” or as

“small-county” receive additional per-pupil funds from the state. Other variation

represents factors such as differences in local revenues, differences in how local

governments choose to spend those revenues, and federal grant program receipts. These

                                                                                                               6 All current expenditures are inflation-adjusted using the urban consumer price index (BLS 2015) to represent real 2013 dollars.

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maps suggest a large degree of heterogeneity in how local entities allocate resources

among different educational purposes, and how the spending patterns change over time.

3. Model of county educational investments

A local education agency (LEA), and its corresponding county governing body,

have many overarching objectives and must make decisions and tradeoffs with these

multiple goals in mind. However, given the current emphasis on test-based

accountability, it is likely that the level of student proficiency on standardized tests is

high on a school district’s list of priorities. For simplicity, we can thus model an LEA’s

objective function as maximizing the aggregate achievement A within county c and year

t. As described above, each county has the authority to allocate yearly local revenues Rt

among a number of different purposes: providing teacher salary supplements, improving

buildings and facilities, paying for other certified and non-certified school personnel, and

paying for other operating expenses. In the basic model below, a county decides how

much to spend on non-instructional (NI) and instructional (I) categories in order to

maximize student achievement, assuming for the moment that local revenues to be used

toward education (R) are exogenously determined.

1      𝑚𝑎𝑥!!"!!,!!"!!

𝐴!"  = 𝑓 𝑁!"!!, 𝐼!"!!,𝑿!"  

𝑠. 𝑡.    𝑁!"!! + 𝐼!"!! ≤ 𝑅!"!! In this equation a vector of other county characteristics Xct also affects student

achievement, and counties are restricted by an annual budget constraint. I assume there is

a one-time lag period between school expenditures and student outcomes.

If I impose linearity and additive separability assumptions of achievement as a

function of the two types of school resources, this optimization problem becomes:

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2      𝑚𝑎𝑥!!"!!,!!"!!

𝐴!"  = 𝛽! + 𝛽!𝑁!"!! + 𝛽!𝐼!"!! + 𝜷!𝑿!" + 𝜇!"  

𝑠. 𝑡.    𝑁!"!! + 𝐼!"!! ≤ 𝑅!"!! For this basic form of education production function, the solution would be:

𝐼!"!! =0  𝑖𝑓  𝛽! > 𝛽!

𝑅!"!!  𝑖𝑓  𝛽! ≥ 𝛽!;  𝑁!" =

0  𝑖𝑓  𝛽! ≥ 𝛽!𝑅!"!!  𝑖𝑓  𝛽! > 𝛽!

In words, counties would choose to allocate all revenues to whichever type of spending –

instructional or non-instructional – is found most effective for raising student

achievement. However, this situation is unrealistic for a number of reasons, including

federal and state requirements, interaction effects between the two types of spending, and

non-linearity in the production function in the form of diminishing returns.

The concept of fiscal substitution, popularized by research on state and local

behavioral responses to federal grant policy in the 1970s (Gramlich & Galper, 1973;

Johnson & Tomola,1977) and more recently in the context of school finance reform

(Baicker & Gordon, 2007), may be relevant toward understanding how county

governments react to state- or federal-imposed fiscal constraints. In North Carolina, the

strict statewide salary schedule and class size requirements leave counties few options for

supplementing classroom instruction through traditional teacher support. If non-

instructional support personnel are complementary to the benefits provided by teachers

(as modeled below), this may strengthen the case that local non-instructional resources

could benecit student learning.

To formalize this simple example in which we allow the impacts of instructional

and non-instructional resources to interact, the problem becomes:

3      𝑚𝑎𝑥!!",!!"

𝐴!"  = 𝛽! + 𝛽!𝑁!" + 𝛽!𝐼!" + 𝛽!(𝐼!"×𝑁!")+ 𝜷!𝑿!" + 𝜇!"  

𝑠. 𝑡.    𝑁!" + 𝐼!" ≤ 𝑅!"

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This problem results in the solution below. Essentially, counties respond to both the

relative efficacy of each type of resource (𝛽! and 𝛽!), and the degree to which the

resource types interact (𝛽!):

𝑁!" , 𝐼!" =𝑅2 +

(𝛽! − 𝛽!)2𝛽!

,𝑅2 −

(𝛽! − 𝛽!)2𝛽!

Figure 2 provides a three-dimensional graphical representation of the associations

between log instructional per-pupil spending, log non-instructional per-pupil spending,

and student math and reading performance at the county-year level. Indeed, we observe

that the county-year observations with highest student test performance tend to have high

expenditures in both categories. On the other end of the spectrum, there also seem to be

counties performing well on standardized tests but with low levels of overall per-pupil

spending. This could perhaps be a “large district effect” wherein larger districts are able

to provide certain services at a lower per-pupil cost due to economies of scale, although

there are numerous alternative explanations.

Without a causal estimation approach, it is impossible to tease out the direct effect

of county education spending priorities on student outcomes. In contrast to school

boards, county commissioners have an array of interrelated objectives, including

promoting the safety, health, and economic prosperity of the entire county population.

Therefore their goals are not as simple as in the decision-making model above, and they

are likely to disagree on the relative effectiveness of different investments. The relative

benefits and costs of non-instructional and instructional resources to student performance,

as estimated causally in this study, could therefore be informative for policy-makers at all

levels of government as they consider how to optimize returns to expenditures.

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My identification strategy, detailed in the next section, arises directly from the

process by which county governments raise revenues and allocate educational and non-

educational expenditures across different functions each year. In particular, due to the

fairly high level of discretion of county commissioners in the budgetary process, I can

take advantage of reliable sources of exogenous variation in instructional and non-

instructional resources at the local governmental level.

4. Empirical approach

Data

This study introduces a new dataset consisting of student-level administrative data

in North Carolina merged with detailed school expenditures data by purpose, type of

expenditure, and revenue source. The dataset includes all 100 counties tracked for 18

years between 1996 and 2013, matched to over 13 million student observations from

grades K-12 during this period. This comprehensive time coverage and large student

sample size allow for very precise estimates of how local education expenditures affect

students across a number of domains. Table 1 depicts descriptive statistics, including

demographic characteristics, parental education, and educational indicators, of a cross-

section of the main student dataset.

Student achievement outcomes for this study include End of Grade test scores in

reading and math for students in grades three through eight, and End of Course test scores

for students from grades nine through twelve in English I; English II; U.S. History;

Economics, Law, and Politics; Civics; Biology; Physical Science; Chemistry; Physics;

Algebra II; and Geometry. All test scores are normalized by grade level, year, and subject

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to have mean zero and standard deviation one. Therefore test score results in the

following sections are presented as effect sizes in terms of test score standard deviations.

For students in grades nine through twelve, I average all normalized science and math

scores for a given student in a given year to construct an annual “sciences” score. I do

the same with English and social studies course scores to construct a “humanities”

measure for each student-year observation.7 Combining across years and grades, the

dataset contains approximately 7.3 million observations for End of Grade scores and 2.5

million observations for End of Course scores.

Recent empirical research has demonstrated the long-term importance of non-

academic personal attributes for educational attainment, labor market outcomes, and

social outcomes (Heckman, Stixrud, & Urzua, 2006). Importantly, a series of recent

studies on teacher quality have shown that administrative behavioral measures can

reliably capture student non-cognitive traits and behaviors (Gershenson, Forthcoming;

Jackson, 2012; Ladd & Sorensen, Forthcoming). Therefore, to the extent possible using

administrative data, this study seeks to measure outcomes indicative not only of

curricular learning but also of non-academic behaviors and traits. I estimate the effects of

expenditures on the following non-test outcomes: attendance, disciplinary infractions,

and self-reported extracurricular participation. Student attendance is measured by a

continuous measure of absences during the school year. A disciplinary infraction measure

equals one if the student received in-school suspension, out-of-school suspension,

expulsion, or placement in an alternative school or alternative learning program that year.

                                                                                                               7 These scores are computed as row means such that the “sciences” score of students with only one sciences/math course score in a given year will be that score and such that the “sciences” score of students with several science/math course scores in that year will be an average of all normalized scores.

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It equals zero otherwise. And an extracurricular participation measure likewise equals

one if a student in ninth through twelfth grade reports participating in an academic,

athletic, artistic, community service, or vocational club in the current academic year. This

measure equals zero if students report that they did not participate in any of these types of

activities that year.

I have matched these student-level outcomes to education expenditures

information from the North Carolina Department of Instruction, also dating back to the

1995-1996 school year. I observe county annual current expenditures, categorized by

purpose code and object code. Accountants use the four-digit purpose codes to designate

how much money schools and districts spend on particular functions.8 The object codes

on the other hand signify the type of spending: salaries, employee benefits, purchased

services, supplies and materials, or instructional equipment. For the purpose of this

analysis, I include only salary expenditures because they reflect the direct effect of

increasing personnel in school and because they are measured more consistently over

time than other categories such as benefits. I adjust all expenditures data for inflation to

2013 equivalent dollars.

Also at the county-year level, this dataset contains a comprehensive set of time-

varying covariates: population estimates and poverty levels from the U.S. Census Bureau;

the local unemployment rate from the Bureau of Labor Statistics; political party

affiliation rates from the State Board of Elections; and yearly total county expenditures

and property assessment values from the County Budget and Tax Survey. These

                                                                                                               8 Instructional spending includes salary expenditures in the purpose code 5100 (Regular instructional programs); Non-instructional spending includes salary expenditures in the following purpose codes: 5820 (Attendance – social work services); 5830 (Guidance services); and 5840 (Health services). Exact descriptions of these categories are provided in Appendix Table A1.

21

economic, political, and population change measures act mostly as control variables in

the estimation framework described below.

Identification strategy

The purpose of this study is to estimate the effects of local non-instructional and

instructional expenditures on student outcomes in grades three through twelve, including

test scores across many subjects, absences, disciplinary infractions, and extracurricular

participation. A standard OLS regression of outcomes on the mix of spending would

likely lead to biased estimates since the county’s level of per-pupil expenditures on

various purposes is endogenous (Haegeland, Raaum, & Salvanes, 2012; Hanushek

1997).9 Three main types of omitted variables likely introduce bias to a regression

model: 1) observable and unobservable characteristics of counties; 2) time trends and

contemporaneous events; and 3) time-varying local economic, political, or population

factors.

To account for the first two sources of endogeneity, I include county and year

fixed effects in all models. This implies that my estimates reflect the effects of within-

county changes in local education spending across time. However, county time-varying

characteristics could still drive both local spending patterns and student achievement

even with county and year fixed effects. For example, counties could respond to local

financial conditions or to problems and shortages as they arise in their schools by

                                                                                                               9  Appendix Table A2 compares IV estimates to traditional OLS estimates for returns to instructional and non-instructional spending. OLS estimates of the effects of education spending appear to be downward biased, consistent with the conclusions of some prior research (e.g. Haegeland, Raaum, & Salvanes, 2012). One plausible explanation is that county commissioners allocate additional instructional or non-instructional funds in response to perceived need of students, which would lead to problems of simultaneity.  

22

increasing education spending in certain categories, but the underlying conditions could

also affect student learning and behaviors.10 Therefore, in addition to the county and year

fixed effects, I employ an instrumental variables approach to account for the nonrandom

allocation of resources within counties across years. The model is further complicated by

the fact that it includes three endogenous variables on the right hand side of the equation:

non-instructional spending, instructional spending, and total county expenditures.

Therefore I need three instrumental variables to provide enough exogenous variation in

local expenditures. For this task I have identified: first, a measure of how recently

property value reassessment took place in the county; second, a measure of the political

party majority of the county board of commissioners; and third, interaction terms of these

two measures. I describe and justify these three exogenous sources of variation in more

detail below.

Revaluation instrument

North Carolina General Statutes require counties to reassess real property values

every eight years, or more frequently if the county so chooses. Each county operates on a

different revaluation schedule, and in revaluation year counties often experience a

noticeable jump in increased property tax revenue (or a dip if average property values

have decreased since the previous revaluation year). Walden (2003) and Ladd (1991)

observe this phenomenon in North Carolina counties, and Bloom and Ladd (1982) found

                                                                                                               10 Findings from a simple regression of education expenditures on county economic conditions suggest that this is likely the case. County-level unemployment claims (lagged by two years) significantly affect education expenditures even when county and year fixed effects are included. The literature on this topic finds that local job loss has detrimental effects on population-level student achievement (Ananat, Gassman-Pines, Francis, & Gibson-Davis, 2011). Therefore omitting key local economic indicators could introduce significant bias into OLS estimates of the effects of county education expenditures on student outcomes.

23

that Massachusetts counties also tend to increase their property tax revenues during

revaluation years.

As seen in Figure 3a, from the recent North Carolina data from 1996 to 2013,

county revenues from property taxes increase by over 40 percent in the year after

revaluation on average. Furthermore, this sudden increase in revenues translates to the

amount that counties ultimately spend on education and other purposes, although the

effect is typically lagged one year (See Figure 3b). I construct an instrumental variable

that equals the number of years since revaluation, and a corresponding measure that

includes the number of years since revaluation squared. An illustration of how these

measures work in practice is provided in Appendix Table A2 for three fictional counties

over a ten year period.

The revaluation instrument as described above significantly predicts per-pupil

total county expenditures and spending on non-instructional and instructional functions

even when controlling for county and time fixed effects and a set of county time-varying

control variables related to population changes and economic conditions. Table 2

presents first stage estimates from this instrument, the political instrument described

below, and interaction terms of each instrumental variable (F1=6,060; F2=9,946;

F3=14,530).11 It is possible that counties begin increasing education expenditures before

revaluation years in anticipation of property values increasing, or that they choose to set

the tax rate in the revaluation year at a “revenue-neutral rate” such that revenue flows

                                                                                                               11 These F-statistics come from first stage estimates in the sample of students in grades 3-8, including student covariates in addition to the county covariates. First stage estimation was replicated in other student samples and at the aggregated county-year level with only 1,800 observations. All instrumental variables remain strong predictors of county spending, even in these alternative samples.

24

remain constant. But in either of these instances, one would expect the effect of property

revaluation on local expenditures to be slightly downward biased.

Political instrument

Political party majority affiliation of the county board of commissioners in the

two years prior to measured school expenditures serves as the second instrumental

variable for this analysis. The county board of commissioners is primarily responsible

for determining annual budgetary allocations and setting local tax rates. These boards

contain either five or seven members, each with four-year terms, and elections are held

every two years. For this reason, the political party majority of a board often switches

back and forth within counties across years.12 In Figure 4, a local polynomial smooth

plot of per-pupil county expenditures (with the 95 percent confidence interval plotted in

gray) shows that for several years preceding political party turnover events, expenditures

are quite stable. However, upon party majority change – in this case from a Republican

to Democratic majority – county expenditures significantly increase. As can be seen in

Figure 5, which graphs the percent of registered voters that are Democrats, political party

turnover events do not appear to be caused by any underlying major political shifts.

This political instrumental variable significantly predicts both the total level of

per-pupil educational spending as well as the proportion allocated to instructional and

non-instructional purposes (See Table 2). As shown in Table 2, Republican-majority

county commissioners tend to spend less in general and less on non-instructional

investments, but more on instructional salary supplements. I assert that the measure of

Republican party majority of county commissioners is unlikely, given the inclusion of                                                                                                                12Sixty-three percent of counties switch political party majority during the observed time period.

25

both county and year fixed effects, to relate to student and youth outcomes through any

mechanisms other than public expenditure. I also control for the annual proportion of

voters registered as Republicans so that, conditional on any underlying political shifts, the

county commissioner political instrument provides truly exogenous variation in local

spending.

Interaction term of political and revaluation instruments

As a third source of exogenous variation, I include two interaction terms of the

two revaluation instrumental variables each multiplied by the political instrumental

variable indicator. As presented numerically in Table 2 and depicted graphically in

Figures 6a through 6c, predicted expenditures have much steeper gradients by years since

property revaluation for Democratic-majority boards of county commissioners than for

Republican-majority boards of county commissioners. This finding implies that

Democratic boards are more likely to take advantage of the timing of property value

reassessment to increase total county revenues. As with the other two identified sources

of variation in local education expenditures, these interaction terms appear to meet all

necessary criteria for instrumental variables (having no correlation with the error term,

and showing strong correlation with the endogenous predictors of interest).

Estimation model

To estimate the effects of non-instructional and instructional salaries on student

outcomes, I use full information generalized two stage least squares estimates of the

system of simultaneous equations (Balestra & Varadharajan-Krishnakumar, 1987). The

26

first stage equations, which predict total county expenditures (minus the two other

categories) Tc,t; non-instructional salaries Nc,t; and instructional salaries Ic,t; for county c

and year t are as follows:

(1a)𝑇!,! = 𝛽! + 𝛽!𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!! + 𝜷𝟏𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏 + 𝜷𝟐(𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!!×𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏)+𝜷𝟑𝑿𝒄,𝒕 + 𝜃! + 𝛿! + 𝜇!,!

(1b)𝑁!,! =

𝛽! + 𝛽!𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!! + 𝜷𝟏𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏 + 𝜷𝟐(𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!!×𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏)+𝛽!𝑋!,! + 𝜃! + 𝛿! + 𝜇!,!

(1c) 𝐼!,! = 𝛽! + 𝛽!𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!! + 𝜷𝟏𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏 + 𝜷𝟐(𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!!×𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏)+

𝛽!𝑋!,! + 𝜃! + 𝛿! + 𝜇!,! Expenditures for these three separate purposes are thus regressed on the political

instrument (𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!!), the vector of revaluation instruments (𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏), and

interaction terms between those measures (𝑃𝑜𝑙𝑖𝑡𝐼𝑉!,!!!×𝑹𝒆𝒗𝒂𝒍𝑰𝑽𝒄,𝒕!𝟏). These first stage

models also include county fixed effects (𝜃!), year fixed effects (𝛿!), and county time-

varying indicators (𝑿𝒄,𝒕) including population estimates, student-age poverty rates,

unemployment rates, assessed property values, registered voter affiliation rates, and

average student characteristics (gender, race/ethnicity, and prior test performance).

From the first stage system of equations, with three endogenous spending

variables and three exogenous instruments, I can therefore predict values for local

expenditures derived from variation in years since property revaluation, political majority

of county government, and interactions between the two. In the second stage, I estimate

the effect of lagged predicted spending in several categories on a student outcome 𝑌!"#:

(2) 𝑌!,!,! = 𝛽! + 𝛽!𝑁!,!!! + 𝛽!𝐼!,!!! + 𝛽!𝑇!,!!! + 𝜷𝟒𝑿𝒊,𝒄,𝒕 + 𝜃! + 𝛿! + 𝜀!,!,!

In this equation, I regress each of student i’s outcomes in year t county c on predicted

non-instructional, instructional, and other county-level spending in the period prior

27

(𝑁!,!!!; 𝐼!,!!!; and 𝑇!,!!!); a vector of student-level covariates including prior test scores,

gender indicators, and race/ethnicity indicators (𝑿𝒊,𝒄,𝒕); and county-level covariates as in

the first-stage equations. Once again, I include county and year fixed effects such that I

exploit only within-county variation over time in education resource allocation.

The timing of how quickly expenditures may affect student learning and

behaviors, as well as the timing of when property revaluation and political shifts

influence local expenditures, are both critical to this model. This analysis assumes that

student outcomes in a certain year are a function of average expenditures in the two years

prior to measurement. Similarly, this study assumes that a one-year lag exists between

local expenditures and their prior predictors (county government political majority

changes and property value reassessment). I perform a number of robustness tests to

ensure that findings in both the first and second stages are not sensitive to the choice of

time lags.13

5. Results

Answering the question of how non-instructional investments affect student

outcomes could inform how schools and local, state, and federal governments in the

future choose to allocate resources effectively. The two-stage model described in the

previous section allows me to estimate the causal impact of increased spending on

teachers and teaching assistants or school social workers, guidance counselors,

psychologists, and health services. I estimate these impacts across a number of domains

                                                                                                               13 I experiment with other lag periods for expenditures to outcomes (0-1 years; 1-3 years; 2-3 years; 3-5 years), and determine that the direction and magnitude of findings are similar when the time lag is anywhere between 1 and 3 years, and nonsignificant with smaller or larger lags.

28

of student performance: math and reading scores in grades 4-8; sciences and humanities

performance in grades 9-12; absences per year; serious disciplinary infractions; and

extracurricular participation in grades 9-12.

Table 2 presents results from the first stage equations. In terms of the property

revaluation instruments, we can note that expenditures in all spending categories increase

shortly after a property value reassessment year, and then decline steadily in the years

following that. Figures 6a, 6b, and 6c show these quadratic trends from the first stage

estimates graphically (separately for Republican-majority and Democratic-majority

boards). One can observe that Republican-majority boards of county commissioners

spend less per-pupil than do Democrat-majority boards of county commissioners. They

also allocate less money per-pupil on non-instructional expenses, although they allocate

more money toward instructional salaries. Interestingly, Republican-majority boards

appear to respond less dramatically to the property revaluation schedule. One could

conclude that they have lower propensity to use the revaluation timing as an opportunity

to increase property tax revenues and public expenditures.

Student achievement outcomes

Moving to second-stage estimation, first I look at the impact of increased non-

instructional and instructional expenditures on student test scores. As can be seen in

Table 3, a $100 increase in per-pupil expenditures on non-instructional services (social

workers, guidance and psychological services, and health services) leads to a 0.067

standard deviation increase in math scores and a 0.014 standard deviation increase in

reading scores in grades 4 through 8. Given the relatively small investment of money,

29

this magnitude of the test score increase is meaningful. The math effect, for example, is

equivalent to one-fifth of the total average difference between sixth grade and seventh

grade math performance. The same dollar increase in instructional salary spending

induces somewhat smaller, but statistically significant, improvements in test performance

(0.016 SD for math and 0.029 for reading).

At the high school level, a $100 per-pupil increase in non-instructional spending

translates to increases in average science and math course performance of 0.099 standard

deviations but no increases in average humanities and social sciences course performance

(See Table 3). The same $100 per-pupil increase in local instructional salary

supplements augments science and math performance in high school by 0.078 standard

deviations. Instructional salary spending also does not affect average humanities and

social sciences performance. The results at the high school level parallel those found at

the elementary school and middle school levels, suggesting that these investments do not

have widely varying impacts by grade level.

As discussed in the methods section, the omission of other county expenditures

from the model (whether educational or non-educational) could bias upwards estimated

effects of increasing instructional or non-instructional salaries. Therefore, I include in the

model total other county expenditures as an endogenous regressor simultaneously with

non-instructional and instructional salaries. As can be seen in Tables 3 and 4, total

county expenditures on other categories appear to have little to no effect on student test-

based or behavioral outcomes. Surprisingly, increasing total county expenditures appears

to have a small but statistically significant negative effect on student reading scores

(Table 3) and positive effect on student absenteeism (Table 4). Although the point

30

estimate magnitudes are small enough to not be too concerning, I cannot conclude

definitively what mechanisms may be generating these results.

The logic behind instructional spending’s impact on student achievement is clear.

Instructional spending can pay for more experienced teachers and attract higher quality

teachers, and it can also subsidize teacher assistants to help in the classroom. These

investments effectively raise student performance, particularly in quantitative subjects.

Why non-instructional spending would have such significant effects on student test

scores is less apparent. The multiple instrumental variables technique identifies effects of

the two endogenous expenditures measures separately, and so collinearity between non-

instructional and instructional spending is unlikely to explain the effect. Providing

students with access to guidance, psychological, social work, and health services may

allow students to focus and participate more fully in classroom learning. To test potential

behavioral mechanisms of the effect, I examine the relation between non-instructional

resources and student absences, disciplinary infractions, and extracurricular participation.

To double-check the robustness of the identification strategy, I test for reverse

causality using a strategy similar to that used by Rothstein (2009) to identify bias in

teacher value-added models. Specifically, I estimate the impact of increasing

instructional or non-instructional salary spending in year t+1 on student outcomes in year

t, applying the same instrumental variables approach and control covariates as before.

Of the eight outcomes measured in grades four through eight, the main per-pupil

spending variables affect only one with marginal significance (See Appendix Table A4).

Other than this one negative impact on reading achievement (significant at the 10%

31

confidence level), the test provides no evidence that other underlying factors may be

driving this study’s main findings.

Student behavioral outcomes

As with student test scores, I estimate the effects of investments in social workers,

guidance and psychological services, and health services on student behavioral outcomes.

Jackson (2014) demonstrates that behavioral outcomes measured in student

administrative data robustly predict adult economic and social outcomes. The first

outcome of interest is student absences. Reported in Table 4, an additional $100 per

pupil on non-instructional services reduces average student absences by 0.57 days per

year (down from the average number of absences for the typical student of 8 days).

Instructional spending of the same quantity also decreases student absenteeism, but by a

smaller amount (0.03 absences). These results are highly policy-relevant because

frequent absence, even as early as the sixth grade, reliably predicts the likelihood of a

student eventually dropping out of school (Allensworth & Easton, 2007; Balfanz, Herzog,

& Mac Iver, 2007).

For disciplinary infractions, a $100 per-pupil increase in non-instructional

spending leads to a 0.98 percentage point decline in the proportion of students who

receive at least one suspension, expulsion, or placement in an alternative learning

program or school during the school year. This decrease is from a baseline rate of 10% of

students incurring such serious disciplinary consequences each year. And finally, for

extracurricular participation in high school, a $100 increase in per-pupil non-instructional

spending produces a 13.9% increase in self-reported participation in academic clubs,

32

sports, arts, community service, or vocational clubs, up from a baseline level of 65%.

Instructional spending has no statistically significant impact on student disciplinary

infractions or on self-reported extracurricular participation. (The non-significant

coefficients on instructional spending are -0.012 for disciplinary infractions and 0.007 for

extracurricular participation.) Table 4 presents main findings for all behavioral

outcomes.

Up to this point I have framed the student behavioral indicators as potential

mediators of the effect of non-instructional resources on student achievement, but I have

not tested this mediation directly. To do so, I can perform structural equation model

(SEM) estimation and through this process tease out direct and indirect effects of

increasing instructional and non-instructional expenditures on student test scores. In the

case of continuous outcome variables and no latent (unobserved) variables, SEM

estimates provide identical results to a three-staged reduced form treatment effect

decomposition used by Heckman, Pinto, and Savelyev in an evaluation of the Perry

Preschool program and other similar research (Heckman, Pinto, & Savelyev, 2013;

Sorensen, Dodge, and the Conduct Problems Prevention Research Group, Forthcoming).

Figures 7a and 7b illustrate the path model for which maximum likelihood

estimation is conducted, correcting for missing data and controlling for student

covariates. This method, unlike the rest of the analysis performed for this paper, relies on

variable covariance rather than on quasi-experimental effects and therefore should be

interpreted with caution. The figures present estimated direct path coefficients for each

one-directional path and indicate that, as expected, increased expenditures are associated

with reduced student absences and disciplinary infractions, which in turn then predict

33

student test scores. Combining direct and indirect effects estimated by the model, non-

academic behaviors explain 30.7 percent of the total effect of instructional spending and

88.6 percent of the total effect of non-instructional spending on math test scores. For

reading achievement, non-academic behaviors account for 19.2 percent of the overall

instructional spending effect and 36.0 percent of the non-instructional spending effect.

Again, this model does not pass the strict exogeneity assumption, but the findings

interestingly suggest that absences and disciplinary infractions play a large role in the

relation between non-instructional salaries and student test scores (and a relatively larger

mediation role than for instructional expenditures).

Heterogeneity by school poverty

In general, these non-instructional services may hold value due to the extent that

they assist students with physical, mental, economic, and personal obstacles to learning.

With this hypothesis in mind, I test whether non-instructional spending has greater

impact in areas with high concentrations of poverty versus areas with low concentrations

of poverty. I define high-poverty counties as those with a student-age poverty rate

greater than 25 percent for most years in the observed sample. Likewise, low-poverty

counties are those with student-age poverty rates below 25 percent for a majority of

years. Table 5 provides estimates of the effects of non-instructional services on student

achievement in grades 4 through 8 for the sample, split by county poverty level.

A $100 increase in 2013 dollars of per-pupil non-instructional spending raises

math achievement by 0.012 standard deviations and reading achievement by 0.004

standard deviations for low-poverty counties (n=5.5 million). This impact is much higher

34

in the high-poverty counties, with increased non-instructional spending associated with

0.239 standard deviations growth in math and 0.077 standard deviations growth in

reading (n=1.9 million). A similar pattern arises for instructional salaries. In low-

poverty counties, a $100 per-pupil investment in instructional salary supplements

increases math scores by 0.004 standard deviations and reading scores by 0.006 standard

deviations; in high-poverty counties these values are 0.065 standard deviations and 0.098

standard deviations. (The math effect for instructional expenditures in high-poverty

counties is not significant.)

Returns to non-instructional spending are nearly 20 times greater for math

performance in high-poverty areas than low-poverty areas, with similar patterns emerging

from reading score results. These estimates suggest that investments in school support

personnel such as social workers, health services, and guidance counselors, in schools

with concentrated low-income student populations could go a long way toward closing

socioeconomic achievement gaps.

Nonlinearity in expenditure effects

Thus far all estimates have represented the average linear effect of supplementing

either instructional or non-instructional resources by 100 additional dollars per pupil.

However, the baseline levels of spending toward instructional and conversely non-

instructional purposes are quite disparate. In 2013, the average North Carolina county

spent $2,491 per pupil on instructional salaries but only $228 per pupil on non-

instructional salaries. Therefore an exogenous $100 boost in expenditures would alter the

non-instructional budget much more dramatically than it would the instructional budget.

35

Furthermore, if there are diminishing marginal returns to education spending, then the

relatively large effects for increasing non-instructional spending may not be so surprising.

To address some of these issues, I explore the possibility of non-linearity in

returns to local education expenditures. To do so, I first estimate the first stage models as

presented in equations 1a, 1b, and 1c, and predict local non-instructional, instructional,

and total county expenditures. For convenience, I focus on just one of the (most salient)

outcomes from the main results: math test score achievement in grades 4 through 8. For

both the math performance outcome and the predicted local spending variables, I demean

each measure by county and year. At this point, I can perform kernel-weighted local

polynomial regression to learn more regarding the non-parametric relationship between

predicted non-instructional and instructional spending and student achievement.

In Figures 8a, 8b, and 8c, I present graphically how predicted local instructional,

non-instructional, and total county spending from the first stage estimates relates to math

performance, as measured in standard deviations from the mean. The marginal effect of

spending more per pupil on local instructional salaries (Figure 8a) appears to be fairly

linear between $0 and $1,500. These estimates are more precise for low levels of

instructional salary spending because a higher number of county-year observations exist

in that range. For non-instructional spending (Figure 8b), an interesting picture emerges.

Any spending within the range of $0 to $50 per pupil appears to have little measurable

effect on student learning; however, moving from spending $50 to spending $100 per

pupil increases math performance by 0.2 standard deviations – a large, rapid increase.

Above $100, the diminishing marginal returns set in and more spending does not lead to

significant math score raises.

36

These non-parametric estimates of the returns to non-instructional resources are

perhaps more informative than the linear estimates. We can observe that the large impact

of providing additional social and health services in schools estimated in this study may

be an artifact of very low baseline spending on these student resources. A small

investment at the county level in non-instructional expenditures (of roughly $100 per-

pupil) could yield large benefits for students, particularly those in high-poverty counties,

but spending above that threshold may not produce any consequential gains. Figure 8c

graphs predicted total county expenditures per pupil (including education expenditures)

against math performance. Although there is a small positive linear effect in the lower

ranges of county expenditures, larger amounts of county expenditures only generate a

noisy net zero effect.

6. Discussion

The primary spending categories examined in this study are of public interest

even without any connection to student learning. Social workers, guidance counselors,

and psychologists provide needed support for children who may be experiencing

educational, mental health, family, or social problems. Health services such as school

nurses, health centers, and dental care, can likewise improve the physical health and

health behaviors of students. However, this study is the first to demonstrate at the

aggregate level that spending on these non-traditional educational categories may

facilitate student learning and improve other behavioral indicators (such as attendance

and disciplinary offenses) predictive of long-term educational success.

37

Corresponding inference about the impact of instructional spending in schools is

limited by the constraints of this study design, due to the fact that I can only look at

effects of instructional salary supplements and of hiring teaching assistants rather than

effects of hiring more teachers per pupil, for example. Local instructional spending,

which again is composed primarily of teacher salary supplements and hiring of teaching

assistants, still appears to modestly boost student learning even in the relative short-term.

The inconsistencies of results in prior school finance research could in part reflect

large heterogeneities in returns to school resources by the type of school resource. For

example, Greenwald, Hedges, and Laine (1996) conclude that the median effect of a $100

increase in per-pupil education expenditures, across an array of former studies, is a 0.002

standard deviation increase in student achievement. The current study, which uncovers

effect sizes larger by an order of magnitude, finds that the marginal effect of increasing

spending on non-instructional or instructional salaries in schools greatly exceeds prior

estimates of returns to school spending, which typically aggregated across a large set of

categories (including for example administration at all levels, retirement and benefits,

capital expenses, and materials). Further research that delves more into the relative

effectiveness of different types of educational spending could provide valuable insight.

Given the serious and growing prevalence of mental health, health, and social-

emotional concerns that K-12 public school students face, perhaps the positive benefits of

school support services are not so surprising. Across the country, states and school

districts are experimenting with “community school” models in which students are

provided comprehensive social, behavioral, and health services, alongside their classroom

activities. A new model in which schools are not only places of instruction but also

38

providers and protectors of social well-being and health of students may in fact make

progress toward closing achievement gaps between low-socioeconomic-status and high-

socioeconomic-status children and youth. Further research on this topic could better

tease out the mechanisms through which non-instructional spending produces change in

students, investigate long-term effects on educational attainment and social outcomes,

and disaggregate the total non-instructional category to assess its components (social

workers and attendance, health services, and guidance counselors and psychologists)

individually.

39

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Figures and Tables Figure 1a. North Carolina per-pupil instructional salary spending: 1996-2013

Figure 1b. North Carolina per-pupil non-instructional salary spending: 1996-2013

Note. These figures are binned scatter plots of median per-pupil spending by county, absorbing county effects. The curve is a quadratic fit plot for the underlying data. Expenditures are adjusted to 2013 dollars. A county is designated as high-poverty if its median poverty rate for individuals aged 5-17 is over 25 percent between 1996-2013, and designated as low-poverty otherwise.

46

Figure 2. Associations between per-pupil spending and student math and reading performance (by county-year observation)

Note. Spending is measured here as log per-pupil current expenditures in 2013 inflation-adjusted dollars. County-level reading and math scores are measured in standard deviations, normalized by subject, grade and year. Each point represents a single county-year observation.

47

Figure 3a. Change in average county-level property revenues by years since property revaluation year

Figure 3b. Change in average county-level expenditures by years since property revaluation year

010

2030

40Pe

rcen

t cha

nge

in p

rope

rty re

venu

es

-4 -2 0 2 4Years since property revaluation

-10

010

20Pe

rcen

t cha

nge

in to

tal c

ount

y ex

pend

iture

s

-4 -2 0 2 4Years since property revaluation

48

Figure 4. County expenditures during Board of County Commissioners political party turnover events (Republican to Democrat)

Note. In this graph the blue line shows a lowess plot of per-pupil total county expenditures before and after a political party switch in the county board of commissioners. The gray lines are 95% confidence intervals.

Figure 5. Registered voter political affiliation during Board of County Commissioners political party turnover events (Republican to Democrat)

7600

7700

7800

7900

8000

8100

Per-

Pupi

l Cou

nty

Expe

nditu

res

-5 0 5Years Since Party Turnover

.348

.35

.352

.354

.356

.358

Perc

ent o

f Reg

iste

red

Vote

rs D

emoc

ratic

-5 0 5Years Since Party Turnover

49

Note. In this graph the blue line shows a lowess plot of the percent of county voters that are registered as Democrats before and after a political party switch in the county board of commissioners. The gray lines are 95% confidence intervals. Figure 6a. Graphed first stage estimates for total county expenditures

Figure 6b. Graphed first stage estimates for instructional salaries

-600

-400

-200

020

0Pe

r-pup

il co

unty

exp

endi

ture

s

0 2 4 6 8Years since revaluation

Republican Democratic

-40

-20

020

4060

Per-p

upil

inst

ruct

iona

l sal

arie

s

0 2 4 6 8Years since revaluation

Republican Democratic

50

Figure 6c. Graphed first stage estimates for non-instructional salaries

Note. For Figures 6a, 6b, and 6c, all predicted values are scaled as their difference in per-pupil expenditures from counties who are in a revaluation year with a Democratic majority board of commissioners.

-40

-20

020

Per-p

upil

non-

inst

ruct

iona

l sal

arie

s

0 2 4 6 8Years since revaluation

Republican Democratic

51

Figure 7a. Mediation model of math test performance: The role of non-academic behaviors in explaining expenditure effects

Figure 7b. Mediation model of reading test performance: The role of non-academic behaviors in explaining expenditure effects

Note. These models are estimated in a structural equation model using maximum likelihood with missing values (MLMV) estimation. Not pictured above, but controlled for in the model, are student demographic characteristics, prior year test scores, and grade and year effects.

52

Figure 8a. Non-parametric effects of predicted instructional expenditures on math performance

Note. The dark solid line represents kernel-weighted local polynomial smoothed regressions. The light solid lines represent 95% confidence intervals. The per-pupil spending variable has been estimated as a function of the vector of instrumental variables, and de-meaned by county and year.

-.20

.2.4

.6M

ath

perfo

rman

ce (S

Ds)

0 500 1000 1500Local instructional spending per-pupil

53

Figure 8b. Non-parametric effects of predicted non-instructional expenditures on math performance

Note. The dark solid line represents kernel-weighted local polynomial smoothed regressions. The light solid lines represent 95% confidence intervals. The per-pupil spending variable has been estimated as a function of the vector of instrumental variables, and demeaned by county and year.

-.10

.1.2

.3M

ath

perfo

rman

ce (S

Ds)

0 50 100 150 200Local non-instructional spending per-pupil

54

Figure 8c. Effect of predicted total county expenditures on math performance (Kernel-weighted local polynomial smoothing)

Note. The dark solid line represents kernel-weighted local polynomial smoothed regressions. The light solid lines represent 95% confidence intervals. The per-pupil spending variable has been estimated as a function of the vector of instrumental variables, and de-meaned by county and year.

-1-.5

0.5

Mat

h pe

rform

ance

(SD

s)

5000 10000 15000 20000 25000Total county spending per-pupil

55

Table 1. Descriptive statistics of student cross-sectional sample (2008-2009) Variable Mean SD Parental education Less than high school 0.051 (0.219) High school graduate 0.389 (0.487) Some college 0.154 (0.361) 4 year degree 0.297 (0.457) Graduate degree 0.109 (0.312) Race/ethnicity White 0.556 (0.497) Black 0.273 (0.446) Hispanic 0.098 (0.297) Other 0.072 (0.258) Behavioral indicators Absences 7.346 (7.849) Disciplinary infractions 0.397 (1.411) Other indicators Limited English Proficiency 0.062 (0.241) Exceptional status 0.112 (0.316) Eligible free/reduced price lunch 0.538 (0.499) Gifted status (ELA) Gifted status (Math)

0.171 0.180

(0.376) (0.384)

Note. Because not all of the student-level covariates above are included during all years of the observed student dataset, I estimate all descriptive statistics instead on a single cross-section of data (the 2008-2009 school year).

56

Table 2. First stage equation results: Effect of county-level instrumental variables on local per-pupil spending by purpose.

Per-pupil local salary expenditures

Non-Instruction Instruction Total county

spending

Years since revaluation 3.637** 14.368** 165.121** (0.070) (0.084) (1.013) Years since squared -0.494** -2.523** -24.087**

(0.010) (0.012) (0.144) Republican majority -17.563** 58.254** -447.528**

(0.170) (0.206) (2.472) Years X Rep majority 6.849** -17.552** -102.590** (0.100) (0.123) (1.457) Squared X Rep majority -0.796** 3.010** 12.771** (0.020) (0.018) (0.216) County fixed effects X X X Year fixed effects X X X F-Statistic 9,946 14,530 6,060 Observations 7,350,836 7,350,836 7,350,836 Number of counties 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.

57

Table 3. Test score IV estimates: Effect of instructional and non-instructional spending on end of grade and end of course achievement.

Grades 4-8:

Math Grades 4-8:

Reading Grades 9-12:

Sciences Grades 9-12: Humanities

$100 per-pupil local spending Non-instructional spending (prior 2 years)

0.067** 0.014+ 0.099** -0.001 (0.006) (0.007) (0.021) (0.002)

Instructional spending (prior 2 years)

0.016** 0.029** 0.078** 0.000 (0.002) (0.001) (0.002) (0.001)

Other county expenditures 0.000 -0.001* 0.000 -0.000 (0.000) (0.000) (0.000) (0.000) County fixed effects X X X X Year fixed effects X X X X Observations 7,766,298 7,332,072 2,319,431 2,527,446 Number of counties 100 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.    

58

Table 4. Behavioral IV estimates: Effect of instructional and non-instructional spending on absences, infractions, and extra-curricular activities

Grades 4-8: Absences

Grades 4-8: Infraction

Grades 9-12: Activities

Per-pupil local spending Non-instructional spending (prior 2 years)

-0.577** -0.988** 0.139** (0.031) (0.061) (0.009)

Instructional spending (prior 2 years)

-0.029** -0.012 0.000 (0.001) (0.000) (0.000)

Other county expenditures 0.005** 0.000+ -0.000 (0.000) 0.000 (0.000 County fixed effects X X X Year fixed effects X X X Observations 13,107,075 2,322,119 3,412,120 Number of counties 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.

 

59

Table 5. Test score IV estimates by county poverty level: Effect of instructional and non-instructional spending on end of grade and end of course achievement.

Grades 4-8: Math

(Low pov.)

Grades 4-8: Reading

(Low pov.)

Grades 4-8: Math

(High pov.)

Grades 4-8: Reading

(High pov.) $100 per-pupil local spending Non-instructional spending (prior 2 years)

0.012** -0.002 0.239** 0.077* (0.002) (0.013) (0.085) (0.036)

Instructional spending (prior 2 years)

0.004** 0.006** 0.065 0.095* (0.001) (0.002) (0.043) (0.041)

Other county expenditures 0.000 -0.000+ 0.020** -0.000 (0.000) (0.000) (0.002) (0.001) County fixed effects X X X X Year fixed effects X X X X Observations 5,481,317 5,472,820 1,857,700 1,854,716 Number of counties 100 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.

60

APPENDIX

Appendix Figure A1. County variation in per-pupil expenditures from 1997 to 2013

Instructional total spending Non-instructional total spending

Legend: Total per-pupil expenditures. Expenditures are inflation-adjusted to 2013 dollars.

   

61

Appendix Table A1. Purpose codes and expenditure definitions

Purpose Label Definition

5100 Regular instructional programs

Instructional activities designed primarily to prepare pupils for activities as citizens, family members, and workers, as contrasted with programs to improve or overcome physical, mental, social, and/or emotional handicaps. Regular instructional programs include grades K-12.

5820 Attendance-social work services

Activities which are designed to improve pupil attendance at school and which attempt to prevent or solve pupil problems involving the home, the school, and the community.

5830 Guidance and psychological services

Activities of counseling pupils and parents, providing consultation with other staff members on learning problems, assisting pupils in personal and social development, assessing the abilities of pupils, assisting pupils as they make their own educational and career plans and choices, providing referral assistance, and working with other staff members in planning and conducting guidance programs for pupils

5840 Health services Physical and mental health services that are not direct instruction. Included are activities that provide pupils with appropriate medical, dental, and nursing services.

Source: NC DPI, 2007

62

Appendix Table A2. Illustration of county revenues instrumental variable for three fictional counties. County 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

A 6 7 0 1 2 3 4 5 6 7 0 B 3 4 5 6 7 0 1 2 3 4 5 C 3 0 1 2 3 0 1 2 3 0 1

The values in each cell reflect the value that the primary Revaluation instrumental variable (years since revaluation) would take in each year and each county for these fictional counties. County A is shown to have revaluation years in 1997 and 2005; county B has a revaluation year in 2000; and county C has three revaluation years: 1996, 2000, and 2004. Most counties perform revaluations only at the required frequency of every eight years, but some choose to do so more frequently. All property revaluation years are set far in advance (typically over a decade).

Appendix Table A3. Comparison of OLS and IV estimates: Effect of instructional and non-instructional spending on end of grade achievement.

Grades 4-8: Math (IV)

Grades 4-8: Reading

(IV)

Grades 4-8: Math (OLS)

Grades 4-8: Reading (OLS)

$100 per-pupil local spending Non-instructional spending (prior 2 years)

0.067** 0.014+ 0.001** 0.004 (0.006) (0.007) (0.000) (0.036)

Instructional spending (prior 2 years)

0.016** 0.029** 0.014** 0.002 (0.002) (0.001) (0.002) (0.000)

County fixed effects X X X X Year fixed effects X X X X Observations 7,766,298 7,332,072 7,344,287 7,332,796 Number of counties 100 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.

   

63

Appendix Table A4. Robustness check: Effect of expenditures in year t+1 on outcomes in year t

Grades 4-8:

Math Grades 4-8:

Reading Grades 4-8: Absences

Grades 4-8: Infractions

$100 per-pupil local spending Non-instructional spending (prior 2 years)

0.001 -0.234+ 0.028 -0.008 (0.013) (0.142) 0.853 (0.029)

Instructional spending (prior 2 years)

0.003 0.015 0.013 0.001 (0.143) (0.013) (0.070) (0.003)

County fixed effects X X X X Year fixed effects X X X X Observations 7,344,287 7,332,796 13,107,075 2,322,119 Number of counties 100 100 100 100 ** p<0.01, * p<0.05, + p<0.1 Robust standard errors in parentheses, clustered by county; covariates include: county population, political, and economic indicators, lagged math and reading scores (for grades 4-8), eighth grade math and reading scores (for grades 9-12), race/ethnicity indicators, gender indicators, and grade indicators.